I am looking for an experience ladder that 'starts' off relatively quickly like a bit of geometric series, then quickly grows like an exponential curve, and then a slow exponetial curve for later levels, in the range of levels 1-5000.
How would I do this mathematically? I am assuming I might just have three sets of equations, but then what is the correct math for getting the level (based on XP), and vice-versa, XP based on level?
I.e., I am thinking something like:
lvl 1 - 10 exp lvl 2 - 12 exp lvl 3 - 15 exp lvl 4 - 18 exp lvl 5 - 22 exp (not quite fibacconi) lvl 6 - 26 exp lvl 7 - 32 exp ... then maybe around level 150 or so it starts growing quickly, like lvl 150 -1000 exp lvl 151 - 1200 exp ... lvl 3000 - 30000 exp lvl 3100 - 40000 exp lvl 4000 - 75000 exp lvl 5000 - 100000 exp
If it's been done, a link would be great (since I am not exactly sure what I am looking for, not quite sure how to find it). Or if it is easy for you to just write the math, please do that too, thanks for your help!